To resolve the low communication rate and susceptible to multipath interference and other issues of pulse modulation communication method, a new scheme of underwater acoustic (UWA) communication was proposed based on fractional Fourier transform (FRFT). Fractional Fourier transform is only applicable to linear frequency modulation (LFM) signal, which has the advantages of high processing gain, long communication distance and less susceptible to interference. The new communication method used LFM signals that divided into groups as coding signals in time domain and decoded by using Pulse Position Modulation (PPM) in fractional domain, and the Rake receiver was presented to suppress the UWA channel's multi-path effect which could lead to intersymbol interference (ISI). This scheme has the characteristic of a high communication rate, the maximum communication rate is up to 800bit/s, and the feasibility and robustness of this system were validated through the simulation results, which is helpful to the long range UWA communication.